Hello, judges and teachers:
I said that the topic of the class is the sum of the internal angles of the triangle, and the content is selected from the first lesson of the seventh section of the seventh grade of nine-year compulsory education published by People's Education Publishing House.
First, the design concept of this lesson under the new round of curriculum reform:
Mathematics is the spiritual communication between people. The communication in classroom teaching is mainly between teachers and students and between students. It needs to use the "dialogue" learning method and adopt a variety of teaching strategies to enable students to develop their own abilities in cooperation, exploration and communication. In the new curriculum, students' feelings, experiences, values and ways to acquire knowledge are contrary to the traditional teaching mode, which is the focus of teachers' search for new teaching methods in the new curriculum. It should be said that with the gradual perspective of teachers on the new curriculum, new teaching methods will form a new path. It is necessary to break the original framework of teaching activities and establish a teaching activity system that adapts to the interaction between teachers and students; Meet students' psychological needs and realize emotional harmony between teachers and students; Give students a chance to experience success and change "I want to learn" into "I want to learn". I think the change of teachers' role will definitely promote the development of students and education. In the future teaching process, what teachers should do is: help students decide appropriate learning goals, and confirm and coordinate the best way to achieve these goals; Guide students to form good study habits and master learning strategies; Create rich teaching situations, cultivate students' interest in learning and fully mobilize students' enthusiasm for learning; Provide all kinds of conveniences for students and serve their study; Establish an acceptable, supportive and tolerant classroom atmosphere; As a participant in learning, share your feelings and ideas with students; Seek truth with students and be able to admit your mistakes and mistakes. The creation of teaching situation is a challenge for teachers after entering the new curriculum. The teaching situation that adapts to the new round of basic education curriculum reform is not agreed in the article, nor can it be used immediately. We need to explore, study, discover and form in the whole process of teaching activities.
Second, teaching material analysis and handling:
The theorem of the sum of internal angles of a triangle reveals the quantitative relationship of the three angles that make up a triangle. In addition, the auxiliary line is introduced in the proof, which lays the foundation for the subsequent study. The theorem of triangle interior angle sum is also the embodiment of algebra of geometric problems.
Third, student analysis.
Students of this age group have the ability to collect, sort out and reform mathematical modeling problems that are suitable for their own use and close to the reality of life. They are willing to try, explore, think, communicate and cooperate, have the ability of analysis, induction and summary, and they are eager to experience success and pride. Therefore, teachers should give students full freedom and space, and at the same time pay attention to the openness and development of the problem.
Fourth, the teaching objectives:
1. Knowledge goal: In situational teaching, through exploration and communication, the "triangle interior angle sum theorem" is gradually discovered, so that students can personally experience the process of knowledge and simply apply it. Be able to explore the quantitative relationship and changing law in specific problems and understand the idea of equations. Try to find solutions to problems from different angles through open-ended propositions. In teaching, through effective measures, students can gain experience in solving problems in the process of reflection and carry out personalized learning.
2. Ability goal: To cultivate students' ability of logical reasoning, bold guessing and hands-on practice through jigsaw puzzles, problem thinking, cooperative exploration and inter-group communication.
3. Moral education goal: Infiltrate the education of aesthetic thought and method by increasing auxiliary line teaching.
4. Emotion, attitude and values: Under the good teacher-student relationship, establish a relaxed learning atmosphere, so that students are willing to learn mathematics, avoid difficulties, gain a successful experience in mathematics activities, enhance their self-confidence and enhance their sense of collective responsibility in cooperative learning.
The establishment of the key points and difficulties of verbs (abbreviation of verb);
1. Emphasis: Exploration and proof of triangle interior angle theorem.
2. Difficulty: Discussion on the proof method of triangle interior angle and theorem (with auxiliary lines).
Six, teaching methods, learning methods and teaching methods:
The teaching mode of "problem situation-modeling-explanation, application and expansion" is adopted.
Use dialogue, try teaching, problem teaching, hierarchical teaching and other teaching methods to achieve the teaching purpose.
Teaching process design:
First, create a situation, suspense introduction
The introduction of new courses is the beginning of communication between teachers and students, the psychological preparation for students to learn new knowledge, and the key to narrowing the distance between teachers and students and getting rid of the psychology of being difficult to learn and boring. Successful lead-in is to make students feel familiar with their own life, so that students can quickly enter the classroom in the shortest time, resulting in great interest and curiosity. Then teaching activities will become a pleasure for them.
Specific practice: throw a question: "What is the angle of the top when the folding ladder (computer display graphics) in the school logistics office is opened?" A student gave the answer immediately after measuring the angle between two ladder legs and the ground. Do you know why? "The student thought for a moment, and I pointed out that you can answer this question after learning this lesson. So as to introduce new courses.
Second, explore new knowledge.
1. Hands-on practice, trying to find that students are required to cut the triangle cardboard prepared in advance according to lines, and then use the cut ∠A and ∠B to make the vertices of the three pieces coincide with the ∠C puzzle in the complete triangle cardboard. What kind of phenomenon can they find? Some students will find that the three are at right angles. At this time, let the students observe each other's puzzles and verify the results. Through observation and communication, we can learn from each other's methods and realize the interaction between life and life. When the communication is sufficient, paste the spelled graphics in groups, and the teacher comments and summarizes the classification. Divide the spelled figure into two situations: ∠A and ∠B are on the same side and both sides of ∠C respectively. Give praise to the team with cooperative spirit.
(Show the puzzle on the blackboard)
2. Try to guess: What did you find from the activity when the teacher asked questions? Adopt the way of intra-group communication to produce thinking collision. At this time, I will go to the students and give appropriate guidance to the disadvantaged groups. After that, the students report their findings in groups. That is, the sum of the three internal angles of a triangle is equal to 180 degrees.
3. Proof conjecture: First, help students recall the basic steps of proposition proof, and then let students finish drawing independently, write out the known and verified steps, and other students supplement and improve. Ask the students to explore the proof method in groups according to the hands-on exercises just now. This link should give students enough time to think, discuss, discover and experience, so that students can learn from each other's strong points, explore together, find the breakthrough point of proof and experience success. Pay more attention to and guide students with learning difficulties, don't give up any students, improve the teacher-student relationship of students with learning difficulties, and lay the foundation for continuing learning. After cooperative exploration, report the proof method and pay attention to standardizing the proof format. The concept of auxiliary line is naturally introduced here. However, it should be noted that adding auxiliary lines is not blind, but in order to prove a conclusion, it is necessary to quote a definition, axiom and theorem, and the original drawing does not have the conditions to use them directly, so it is necessary to add auxiliary lines to create conditions and achieve the purpose of proof.
4. Use what you have learned and practice according to the feedback.
(1) In △ABC, it is known that ∠ A = 80. Can you know the degree of ∠B+∠C?
Solution: ∫∠A+∠b+∠C = 180 (triangle interior angle sum theorem)
∴∠ b+∠ c = 100 in △ABC
(2) If ∠ A = 80 and ∠ B = 52, then ∠C=?
Solution: ∫∠A+∠b+∠C = 180 (triangle interior angle sum theorem)
∠∠A = 80∠B = 52 (known)
∴∠C=48
(3) In △ABC, ∠ A = 80, ∠ B-∠C= 40, then ∠C=?
(4) Given ∠A+∠B = 100∠C = 2∠A, can we find the number of times ∠A, ∠B and ∠C?
(5) In △ABC, ∠A: ∠B: ∠C = 1: 3: 5 is known. Can you find the degree of ∠ A, ∠ B and ∠ C?
Solution: Let ∠ A = X, then ∠ B = 3x, ∠ C = 5x.
X+3x+5x= 180, which is derived from the theorem of sum of interior angles of triangles.
Solution, x=20
∴∠A=20 ∠B=60 ∠C= 100
(6) It is known that in △ABC, ∠C=∠ABC=2∠A, how to find the number of (1)∠B? (2) If BD is the height of AC side, what is the degree of ∠DBC?
Question (6) is adapted from the examples in the book. This question is typed by an auxiliary courseware with auxiliary lines, giving students an intuitive graphical demonstration from simple to complex.
Through this group of exercises, we can infiltrate the idea of simplifying graphics, continue to infiltrate the idea of unity, and solve geometric problems with algebraic methods.
5. Consolidate and improve, student-oriented.
(1) As shown in the figure: B, C and D are on a straight line, ∠ ACD = 105, and ∠A=∠ACB, then ∠B =- degrees.
(2) As shown in the figure, AD is the bisector of △ABC, and ∠ B = 70 and ∠ C = 25, then ∠ADB =- degree, ∠ADC =- degree.
This group of exercises is a comprehensive application of triangle interior angle sum theorem, angle definition and angle bisector, which can cultivate students' ability to analyze and solve problems and help them gain some experience.
6. Expansibility, openness and divergence of thinking
As shown in the figure, it is known that at △PAD, ∠ APD = 120, b and c are points on AD, and △PBC is an equilateral triangle. Try to find out the relationship between geometric quantities.
This topic aims to stimulate students' independent thinking and innovative consciousness, cultivate innovative spirit and practical ability, and develop individual thinking.
Thirdly, induction, assimilation and adaptation.
1. Students talk about experience
2. The teacher summarized and showed the main points of this part.
3. The teacher's comments give affirmation and hope to the students' active cooperation in class.
Fourth, homework:
1。 Required questions: Question 3. 1, 10, 1 1, 12.
2. Selection question: Question 3. 1, 13, 14.
Five, the blackboard design
Sum of internal angles of triangle
Student puzzle known: verification:
Proof: Open-ended question:
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